At this time, the file types available for import to QuickBooks Online (QBO) are CSV, Google Sheets, and XLS/XLSX.
An option I can provide you is to look for a third-party app that can convert your IIF file to any of those accepted file types I stated above. You can also search for a third-party app that can directly import the IIF file to your QBO company.
For both options, feel free to check out this page for a complete list of third-party apps that you can sync with QBO: QuickBooks Apps Store.
QuickBooks .iif files can be opened using Microsoft Excel and saved as spreadsheets (.xls, .xlsx) without any trouble.
Open Excel and open the saved IIF file using the Text Import Wizard. Choose File and Save As. Select the Save as type and Microsoft Office Excel Workbook (.xls). Change the file name to remove the quotation marks and the IIF file extension. Excel will automatically add the correct .xls file extension. Click Save
You may need an importer tool to import some transaction types (e.g sales receipts, journal entries).